Pre-exponent

The frequency of the film rupture is the product of the exponent and preexponent. So far we have concerned ourselves with the exponent term. The preexponent of nucleation phenomena is dependent on the mechanism of the growth of the nuclei. Thus, for the growth of a nucleus of a new phase in a supersaturated solution, the pre-exponent is controlled by the rate of diffusion of the molecules to the growing nucleus. For the growth of a neck in an emulsion film, the pre-exponent can be expected to be determined by the viscous flow of the liquid under the action of surface tension. From scaling arguments, one concludes  

In spite of the considerable dependence of the pre-exponent on spontaneous curvature and therefore on temperature, this effect is still minor with respect to the temperature dependence of the exponent, which justifies the evaluation of the activation energy from the Arrhenius plot, with the balanced point region and the region of elevated temperatures treated separately. 

A characteristic example of the macroemulsion stability dependence on the surfactant concentration is shown in Fig. 7.25a and involves almost the same system as the one discussed above, with the oil changed for -heptane. The experiments were conducted at 20 C, where the system above the CMC is in the Winsor I state and tends to form 0/W emulsions. The transition from very 

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For catalytic reactions and systems that are related through Sabatier-type relations based on kinetic relationships as expressed by Eqs. (1.5) and (1.6), one can also deduce that a so-called compensation effect exists. According to the compensation effect there is a linear relation between the change in the apparent activation energy of a reaction and the logarithm of its corresponding pre-exponent in the Arrhenius reaction rate expression. 

From Eq. (1.17b) the apparent activation energy as well as the pre-exponent can be readily deduced. They are given in Eq. (1.19). 

A reaction with a high activation energy tends to have a weaker interaction with the surface and hence will have enhanced mobihty that is reflected in a larger activation entropy. For this reason, the pre-exponents of surface desorption rate constants are lO — lO larger than the pre-exponents of surface reaction rates. 

In classical reaction rate theory expressions, this directly follows from the frequency-pre-exponent relationship ... 

A high frequency of vibration between surface and reactant implies a strong bond, which will give a high activation energy. Hence, increase in pre-exponent and corresponding activation energies counteract Equation (1.21) is the rate expression... 

Name Molec. Density Cristal- Type of Temp. Diffusion Pre-expon. Activation ... 

Name Molec. weight Mr Density (°C) Pp Cristal- linity Type of diffusion coefficient Temp, range of experim. Diffusion coefficient (23 °C) DeXp (cm2/s) x 10 8 Pre-expon. coefficient lg Do Activation energy Ed ... 

Experiment Type of Temp, diffusion range of coefficient experim. (°C) Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy (23 °C) lg D0 Ed Dexp (cm2/s) x 10-8 - (kJ/mol) ... 

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